Gas Laws: Chapter 10
• Force that acts on a given area.
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Gas molecules fill container.
Molecules move around and hit sides.
Collisions are the force.
Container has the area.
Measured with a barometer.
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1 atmosphere = 760 mm Hg
1 mm Hg = 1 torr
1 atm = 101,325 Pascals = 101.325 kPa
Can be used as conversion factors
• Example: What is 724 mm Hg in kPa?
– in torr?
– in atm?
• Experiments have shown that Temperature,
Pressure,Volume, and the amount of substance
are needed to show the physical condition of a
gas
• Equations that represent this are the gas laws.
• Pressure and volume are inversely related at
constant temperature.
• PV= k
• As one goes up, the other goes down.
• P1V1 = P2 V2
• Sketch a graph to represent this kind of
relationship
V
P (at constant T)
V
Slope = k
1/P (at constant T)
22.41 L atm
PV
CO2
O2
P (at constant T)
• 20.5 L of nitrogen at 25ºC and 742 torr are
compressed to 9.8 atm at constant T. What is
the new volume?
• 30.6 mL of carbon dioxide at 740 torr is
expanded at constant temperature to 750 mL.
What is the final pressure in kPa?
• 20.5 L of nitrogen at 25ºC and 742 torr are
compressed to 9.8 atm at constant T. What is
the new volume?
• Answer: 2.0 L Nitrogen
• 30.6 mL of carbon dioxide at 740 torr is
expanded at constant temperature to 750 mL.
What is the final pressure in kPa?
• Answer: 4.0 kPa Carbon Dioxide
• Volume of a gas varies directly with the
absolute temperature at constant pressure.
• V = kT (if T is in Kelvin)
• V1 = V2
T1 = T2
• Sketch a graph to demonstrate this type of
relationship
He
CH4
V (L)
H2O
H2
-273.15ºC
T (ºC)
• What would the final volume be if 247 mL of
gas at 22ºC is heated to 98ºC , if the pressure
is held constant?
• What would the final volume be if 247 mL of
gas at 22ºC is heated to 98ºC , if the pressure
is held constant?
• Answer: 311 mL
• At what temperature would 40.5 L of gas at
23.4ºC have a volume of 81.0 L at constant
pressure?
• At what temperature would 40.5 L of gas at
23.4ºC have a volume of 81.0 L at constant
pressure?
• Answer: 593 K
• Avogadros’ Hypothesis: Equal volumes of gases
at the same temperature and pressure contain
equal numbers of molecules.
• 22.4 L = 6.02 x 1023 molecules
• At constant temperature and pressure, the
volume of gas is directly related to the
number of moles.
• V = k n (n is the number of moles)
• V1 = V2
n 1 = n2
• At constant volume, pressure and absolute
temperature are directly related.
• P = kT
• P1 = P 2
T1
T2
• If the moles of gas remains constant, use this
formula and cancel out the other things that
don’t change.
• P1 V1 = P2 V2
.
T1
T2
• A deodorant can has a volume of 175 mL and
a pressure of 3.8 atm at 22ºC. What would the
pressure be if the can was heated to 100.ºC?
• What volume of gas could the can release at
22ºC and 743 torr?
• A deodorant can has a volume of 175 mL and
a pressure of 3.8 atm at 22ºC. What would the
pressure be if the can was heated to 100.ºC?
• Answer: 4.8 atm
• What volume of gas could the can release at
22ºC and 743 torr?
• Answer: 680 mL
• PV = nRT (“pivnert”)
• If we have “standard conditions”, where
V = 22.41 L at 1 atm, 0ºC, n = 1 mole, what is
R?
• R is the ideal gas constant.
• R = 0.08206 L atm/ mol K
• Tells you about what a gas is NOW.
• The other laws tell you about a gas when it
CHANGES
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R= 0.0821 L atm / mol K
R= 8.314 J / mol K
R = 1.987 cal / mol K
R=8.314 m3 Pa / mol K
R=62.36 L torr / mol K
• A hypothetical substance - the ideal gas whose
pressure, volume, and temperature is
completely described by the equation
• Think of it as a limit: Gases only approach
ideal behavior at low pressure (< 1 atm) and
high temperature.
• Even though gases are not ideal, use the laws
anyway, unless told to do otherwise because
they give good estimates.
• A 47.3 L container containing 1.62 mol of He is
heated until the pressure reaches 1.85 atm.
What is the temperature?
• Kr gas in a 18.5 L cylinder exerts a pressure of
8.61 atm at 24.8ºC What is the mass of Kr?
• A sample of gas has a volume of 4.18 L at 29ºC
and 732 torr. What would its volume be at
24.8ºC and 756 torr?
• A 47.3 L container containing 1.62 mol of He is
heated until the pressure reaches 1.85 atm.
What is the temperature?
• Answer: 658K
• Kr gas in a 18.5 L cylinder exerts a pressure of
8.61 atm at 24.8ºC What is the mass of Kr?
• Answer: 6.51 moles = 546 g Kr
• A sample of gas has a volume of 4.18 L at 29ºC
and 732 torr. What would its volume be at
24.8ºC and 756 torr?
• Answer: 3.99 L
1. Determine the volume of a container at 2.5 atm
and 30. oC if the same gas occupies only 3.0 L at
a pressure of 1 atm and 20. oC.
2. Chlorine gas occupies a volume of 25 mL at 300.
K. What volume will it occupy at 600. K?
3. A sample of hydrogen at 1.5 atm had its
pressure decreased to 0.50 atm producing a new
volume of 750 mL.What was its original volume?
4. Find the number of grams of CO2 that exert a
pressure of 785 torr at a volume of 32.5 L and a
temperature of 32 oC.
• The density of a gas can be determined:
• The higher the pressure and molar mass, the
more dense the gas
• To determine Molar Mass of a gas:
• What is the density of ammonia at 23ºC and
735 torr?
• A compound has the empirical formula CHCl.
A 256 mL flask at 100.ºC and 750 torr
contains .80 g of the gaseous compound. What
is the molecular formula?
• Reactions happen in moles
• At Standard Temperature and Pressure (STP, 0ºC
and 1 atm) 1 mole of gas occupies 22.42 L.
• If not at STP, use the ideal gas law to calculate
moles of reactant or volume of product.
• Mercury can be achieved by the following
reaction
heat
HgO  Hg(l) + O 2 (g)
• What volume of oxygen gas can be
produced from 4.10 g of mercury (II)
oxide at STP?
• At 400.ºC and 740 torr?
• Using the following reaction
NaHCO 3 (s) + HCl 
NaCl(aq) + CO 2 (g) +H 2 O(l)
• Calculate the mass of sodium hydrogen
carbonate necessary to produce 2.87 L of
carbon dioxide at 25ºC and 2.00 atm.
• If 27 L of gas are produced at 26ºC and
745 torr when 2.6 L of HCl are added what is
the concentration of HCl?
• Consider the following reaction
4NH 3 (g) + 5 O 2 ( g )  4 NO(g) + 6H 2 O(g)
• What volume of NO at 1.0 atm and 1000ºC
can be produced from 10.0 L of NH3 and
excess O2 at the same temperture and
pressure?
• What volume of O2 measured at STP will be
consumed when 10.0 kg NH3 is reacted?
4NH 3 (g) + 5 O 2 ( g )  4 NO(g) + 6H 2 O(g)
• What mass of H2O will be produced from
65.0 L of O2 and 75.0 L of NH3 both
measured at STP?
• What volume Of NO would be produced?
• What mass of NO is produced from 500. L
of NH3 at 250.0ºC and 3.00 atm?
• The total pressure in a container is the sum of
the pressure each gas would exert if it were
alone in the container.
• The total pressure is the sum of the partial
pressures.
• Partial Pressure: The pressure exerted by a
particular component in a mixture of gases
• PTotal = P1 + P2 + P3 + P4 + P5 ...
• For each P = nRT/V
• PTotal = n1RT + n2RT + n3RT +...
V
V
V
• In the same container R, T and V are the same.
• PTotal = (n1+ n2 + n3+...)RT
V
• PTotal = (nTotal) RT
V
• Mole Fraction: the dimensionless number that
expresses the ratio of moles of a component
substance to the total moles in a mixture.
• symbol is Greek letter chi
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c1 =
n1
nTotal
= P1
PTotal
c
• The partial pressure of nitrogen in air is 592
torr. Air pressure is 752 torr, what is the mole
fraction of nitrogen?
• What is the partial pressure of nitrogen if the
container holding the air is compressed to
5.25 atm?
• The partial pressure of nitrogen in air is 592
torr. Air pressure is 752 torr, what is the mole
fraction of nitrogen?
• Answer: 0.787234
• What is the partial pressure of nitrogen if the
container holding the air is compressed to
5.25 atm?
• Answer: 4.13 atm
• Collecting Gases over Water: commonly used so
that pressure inside and outside can be equalized.
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Ptotal
= Pgas + PH2O
Atmospheric pressure
• If equalization does not occur, then the pressure
difference must be accounted for as well
Standard values published
based on temperature
• N2O can be produced by the following
reaction
heat
NH 4 NO 3 ( s)  NO 2 (g) + 2H 2 O ( l )
• What volume of N2O collected over water at
a total pressure of 94 kPa and 22ºC can be
produced from 2.6 g of NH4NO3? ( the vapor
pressure of water at 22ºC is 21 torr)
• Theories tell why the things happen.
• Explains why ideal gases behave the way they do.
• Assumptions that simplify the theory, but don’t
work in real gases:
1 The particles are so small we can ignore their
volume.
 The particles are in constant motion and their
collisions cause pressure.
 The particles do not affect each other, neither
attracting or repelling.
 The average kinetic energy is proportional to
the Kelvin temperature.
• To describe temperature, we need the formula
KE = 1/2 mv2
• (KE)avg = 3/2 RT
• This the meaning of temperature – the
average kinetic energy of the particles of a
substance
• the root mean square velocity is
¯
• u2
=u
rms
• (KE)avg = NA(1/2 mu 2 )
• (KE)avg = 3/2 RT
• (KE)avg = NA(1/2 mu 2 )
• (KE)avg = 3/2 RT
3RT
u rms =
M
• Where M is the molar mass in kg/mole, and R
has the units 8.3145 J/Kmol.
• The velocity will be in m/s
• Calculate the root mean square velocity of
carbon dioxide at 25ºC.
• Calculate the root mean square velocity of
hydrogen at 25ºC.
• Calculate the root mean square velocity of
chlorine at 25ºC.
• Practice: Kinetic Molecular Theory.pdf
• The less massive the gas, the higher the speed
• Effusion: the escape of gas through a tiny hole
into evacuated space
• Diffusion: the spread of a substance
throughout a given volume or throughout
another substance
• Graham’s Law: the rate of effusion is inversely
proportional to the square root of the mass of
its particles.
• A compound effuses through a porous cylinder
3.20 time faster than helium. What is it’s molar
mass?
• If 0.00251 mol of NH3 effuse through a hole in
2.47 min, how much HCl would effuse in the
same time?
• A sample of N2 effuses through a hole in 38
seconds. what must be the molecular weight of
gas that effuses in 55 seconds under identical
conditions?
• Please solve problem 10.53 from your
problem set.
• Please solve problem 10.57 from your
problem set.
• Ideal gases are assumed to occupy no space
and have NO attractions for one another.
• Real gases have finite volumes and DO attract
one another
• Engineers and chemists that work with gases
at high pressures cannot use the ideal gas law
because the gases are not “ideal” at these
conditions and must correct for volume
Correction
for volume
of molecules
Correction for
molecular
attraction
Where a and b are Van der Waals constants
which differ for each type of gas
• a and b generally increase with an increase in
mass of the molecule and with an increase in
complexity of its structure (polarity)
• Larger more massive molecules have larger
volumes and greater intermolecular attractive
forces
• Calculate the pressure exerted by 0.5000 mol Cl2 in
a 1.000 L container at 25.0ºC
• Using the ideal gas law and Van der Waal’s equation
– a = 6.49 atm L2 /mol2
– b = 0.0562 L/mol
1. Use stoichiometry to convert the mass of magnesium to
moles of Hydrogen.
2. Convert your measured temperature of the water bath to
Kelvin.
3. Calculate the pressure of the hydrogen gas:
Phydrostatic = Hydrostatic difference (mm)÷ 13.6 (density of Hg)
** note the units from hydrostatic pressure are in mmHg.
You will need to convert these to Pa)
PH2O read from table below.
Patm= use current weather data (up-to-date info from noaa)
Patm = PH2 + P H2O + Phydrostatic
4. Convert Volume of H2 gas to liters.
5. Calculate the value of R using the ideal gas law.
6. Calculate your error based on the published value for the
universal gas constant.
PAY CLOSE ATTENTION TO UNITS!